Can you narrow down "different items" to a range?
Pens, small bowls, pepper mills, bottle stoppers, etc., can be handled by a mini lathe or midi lathe, and benchtop models would be ok.
If you want to turn larger items -- bowls 8" plus diameter, platters, table legs, or bannister newels -- you'll probably need a "full size" lathe (12" swing or greater, 30" or greater between centers).
For flag poles or ships' masts you'll need lots of room.
Whatever size lathe you choose, remember the safety equipment you will need -- something to filter dust, something to protect your eyes, and something to protect your entire face. I use safety glasses *and* a Trend Air full-face respirator (which gives me face protection and dust filtration in one unit). Many woods create dust which causes allergic reactions if inhaled.
I don't find a dust collector works particularly well when turning -- but it makes cleaning up afterwards easier.